We demonstrate a construction that will densely embed a Moore space into a Moore space with the Baire property when this is possible. We also show how this technique generates a new ‘if and only if’ condition for determining when Moore spaces can be densely embedded in Moore spaces with the Baire property, and briefly discuss how this condition can can be used to generate new proofs that certain Moore spaces cannot be densely embedded in Moore spaces with the Baire property.

This paper presents a theoretical investigation into the forced oscillations produced in an elongated lake by wind stresses varying in time. Analysis of the appropriate hydrodynamical equations of motion, in the absence of friction, and the equation of continuity give an estimate of the response function of the longitudinal component of the wind stress onto water level. Two mathematical models are used, one giving an analytical solution and the other requiring numerical methods for solution. The first model assumes that the lake is a homogeneous rectangular body of water and the second uses the mean depth h(x) and area of cross section A(x), considered as functions of distance x directed along the longitudinal axis of the lake.

Generalizing the concept of right bounded rings, a module MR is called bounded if annR(M/N)≤eRR for all N≤eMR. The module MR is called fully bounded if (M/P) is bounded as a module over R/annR(M/P) for any ℒ2-prime submodule P◃MR. Boundedness and right boundedness are Morita invariant properties. Rings with all modules (fully) bounded are characterized, and it is proved that a ring R is right Artinian if and only if RR has Krull dimension, all R-modules are fully bounded and ideals of R are finitely generated as right ideals. For certain fully bounded ℒ2-Noetherian modules MR, it is shown that the Krull dimension of MR is at most equal to the classical Krull dimension of R when both dimensions exist.

In this note, we prove that if a torsion group G has an Abelian subgroup B such that G/B is Abelian and R is a G-adapted ring with the property that R (G/B) has only trivial units then G has the normaliser property in RG.

We show that, for any positive integers n and m, if a set S ⊂ Rm intersects every m − 1 dimensional affine hyperplane in Rm in exactly n points, then S is not an Fσ set. This gives a natural extension to results of Khalid Bouhjar, Jan J. Dijkstra, and R. Daniel Mauldin, who have proven this result for the case when m = 2, and also Jan J. Dijkstra and Jan van Mill, who have shown this result for the case when n = m.

The modified Hankel transform arises naturally in connection with certain semigroup operations on measures in probability theory. We give a tauberian theorem for this transform when certain higher moments exist. The probabilistic significance of our result is that it translates a regularity condition on the transform into a direct condition on the measure. This complements earlier results by Pitman and Bingham for the trigonometric and the modified Hankel transform respectively.

In this paper we define Weyl semiparallel ( · h = 0) and Weyl 2-semiparallel ( · h = 0) submanifolds. We consider n-dimensional normally flat submanifolds satisfying these curvature conditions in (n + d)-dimensional Euclidean space n+d. We also consider normally flat submanifolds in (n + d)-dimensional Euclidean space n+d satisfying the condition  · h = LQ (g, h) and  · h = LQ(g, h).

Let G be a group of collineations in a protective plane Π of order n. Suppose that one of the point orbits of G is an oval of Π, and that G acts regularly on this orbit. We prove that G fixes a non-incident point-line pair if either n is even, or n is odd and G is abelian, or n ≠ 11, 23, 59 is odd and is a pseudo-conic. It is then easy to deduce information about the lengths of the other orbits of G, and about the structure of G as an abstract group.

In this paper we consider a nonlinear parabolic equation with gradient dependent nonlinearities of the form

0 < p, q and a, b ∈ ℝ, with homogeneous boundary condition in a bounded domain Ω ⊆ ℝ,N. In the case 0 < p, q ≤ 1 we prove the existence of solution for suitable initial data. A comparison theorem for the solutions with respect to supersoultions and subsolutions is proved. Using these result, uniqueness and boundedness of solutions is studied.

We consider Stavskaya’s process, which is a two-state probabilistic cellular automaton defined on a one-dimensional lattice. The state of any vertex depends only on itself and on the state of its right-adjacent neighbour. This process was one of the first multicomponent systems with local interaction for which the existence of a kind of phase transition has been rigorously proved. However, the exact localisation of its critical value remains as an open problem. We provide a new lower bound for the critical value.

We show that for a bounded subset $A$ of the $L_{1}(\unicode[STIX]{x1D707})$ space with finite measure $\unicode[STIX]{x1D707}$, the measure of weak noncompactness of $A$ based on the convex separation of sequences coincides with the measure of deviation from the Banach–Saks property expressed by the arithmetic separation of sequences. A similar result holds for a related quantity with the alternating signs Banach–Saks property. The results provide a geometric and quantitative extension of Szlenk’s theorem saying that every weakly convergent sequence in the Lebesgue space $L_{1}$ has a subsequence whose arithmetic means are norm convergent.

A theorem proved by de Leeuw for Γ = Rn and later generalized by Lohoué and Saeki states that if Γ is an LCA group, Γ0 a closed subgroup thereof, π the canonical mapping from Γ onto Γ/Γ0 and Φ a Fourier multiplier of type (p, p) on Γ/Γ0, then Φ ० π is a Fourier multiplier of type (p, p) on Γ. We show here that if 1 ≤ p < q ≤ ∞, Γ and Φ is a Fourier multiplier of type (p, q) on Γ/Γ, then Φ ० π is a Fourier multiplier of type (p, q) on Γ and if Γ0 is a non-compact subgroup of Γ and Φ ० π is a Fourier multiplier of type (p, q) on Γ for some p and q satisfying 1 ≤ p ≤ q ≤ ∞, then Φ is zero. We prove also that if Φ is a Fourier multiplier of type (p, q) and Γ/Γ0, whee 1 ≤ q < p ≤ ∞ and Γ is discrete, then Φ ० π is a Fourier multiplier of type (p, q) on Γ.

We provide a criterion for midpoint locally uniformly rotund renormability of normed spaces involving the class of σ-slicely continuous maps, recently introduced by Moltó, Orihuela, Troyanski and Valdiva in 2003. As a consequence of this result, we obtain a theorem of G. Alexandrov concerning the three space problem for midpoint locally uniformly rotund renormings of Banach spaces.

We study the space of irreducible representations of a crossed product ${C}^{\ast } $-algebra ${\mathop{A\rtimes }\nolimits}_{\sigma } G$, where $G$ is a finite group. We construct a space $\widetilde {\Gamma } $ which consists of pairs of irreducible representations of $A$ and irreducible projective representations of subgroups of $G$. We show that there is a natural action of $G$ on $\widetilde {\Gamma } $ and that the orbit space $G\setminus \widetilde {\Gamma } $ corresponds bijectively to the dual of ${\mathop{A\rtimes }\nolimits}_{\sigma } G$.

The remark is that the recent work in this Bulletin dealing with the extension of a partial to a total strict order on a module over a partially ordered ring falls under standard order extension results for operator groups once it is noted that the added requirement of strictness just comes to injective operation of the positive scalars. These standard results are in turn generalized to a universal algebra setting.

Using a slight generalisation of Brown's inequality, we show that for martingales the existence of a weak nonuniform bound on the rate of convergence in the central limit theorem yields the usual upper bound part of the law of the iterated logarithm.

A hermitian algebra is a unital associative ℂ-algebra endowed with an involution such that the spectra of self-adjoint elements are contained in ℝ. In the case of an algebra 𝒜 endowed with a Mackey-complete, locally convex topology such that the set of invertible elements is open and the inversion mapping is continuous, we construct the smooth structures on the appropriate versions of flag manifolds. Then we prove that if such a locally convex algebra 𝒜 is endowed with a continuous involution, then it is a hermitian algebra if and only if the natural action of all unitary groups Un(𝒜) on each flag manifold is transitive.

Motivated by some earlier Diophantine works on triangular numbers by Ljunggren and Cassels, we consider similar problems for general polygonal numbers.

Recently in this journal we have shown the similarity between the Kleinecke-Shirokov theorem for subnormal operators and the Fuglede-putnam theorem. The purpose of this paper is to show that this similarity can be generalized to operators which belong to some classes of non-normal operators wider than the class of subnormal operators.

Let f be a smooth nonconstant function defined on an n dimensional ball and zero on the boundary n − 1 dimensional sphere. It is shown that the graph of f is a spherical cap (1) if f is positive and if the ratio Hk/Hr is a nonzero constant for 1 ≤ k < r ≤ n on the graph of f or (2) if the ratio Hn/Hk is a nonzero constant on the graph of f.